How is the sentence "10 more than p is -3" written as an equation
p-3 = 10
p+10=-3
p+10=3
p 10-3
The equation for the sentence 10 more than p is -3" will be B. p + 10 = -3.
How to calculate the value?It should be noted that an equation illustrates the relationship between the variables that are given.
In this case, the equation for the sentence 10 more than p is -3" will be:
p + 10 = -3
p = - 3 - 10
p = -13
The value of P is -13.
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I need help with this question
The direction of the resultant vector is 58 degrees east-north if the mouse walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
It is given that:
A mouse is trapped in a maze.
He walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.
Based on the data given:
tanA = 8/(-10+15) = 8/5
A = tan⁻(8/5)
A = 58 degrees
The direction will be 58 degrees east-north
Thus, the direction of the resultant vector is 58 degrees east-north if the mouse walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.
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I’m confused! About this whole thing can someone help me
Answer:
Step-by-step explanation:try using quizlet
51 is a multiple of 2,3,5,6,9,10 or none
Based on the numbers given, we can say that 51 is a multiple of 3.
What is 51 a multiple of?51 is not a prime number which means that it has factors and it is a multiple of several numbers.
The factors of 51 include:
1, 3, 17, and 51
Out of the numbers given of 2,3,5,6,9,10, it therefore means that 51 is a multiple of only one number which is 3. When 3 is multiplied by 17, it gives 51.
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oml i need help with this
Answer:
[tex]2x^{4} - 3x^{2} + 7x[/tex]
Step-by-step explanation:
Brianna practices the piano for 30 minutes per day. Write an expression for the number of hours she practices after n days.
Find the number of hours Brianna practices in 2, 4, and 10 days.
(Thank you in advance for helping me)
Answer: 1/2 * n
1 hour of practice in 2 days
2 hours of practice in 4 days
5 hours of practice in 10 days
Step-by-step explanation:
60 minutes=1 hour
30 minutes * 1 hour/60 minutes=
30*1/60=
30/60=1/2 hour.
1/2 * n
1/2 * 2 = 1 hour of practice in 2 days
1/2 * 4 =
4/2 = 2 hours of practice in 4 days
1/2 * 10=
10/2 = 5 hours of practice in 10 days
An open rectangular box (no top) with volume 9 cubic meters has a square base. Express the surface area S of the box as a function of the length x of one of the sides.
In linear equation, S = x2 + 36/x the surface area S of the box as a function of the length x of one of the sides.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Let x = length of the sides of the base, and h = the height. The volume is given as 9 m3
Volume = area of base * height
9 = x2*h
So 9/x2 = h
The surface area, S, of the box is:
S = (Area of Base) + 4*(Area of a Vertical Side)
S = x2 + 4 * (xh)
Substitute 5/x2 in place of h:
S = x2 + 4 * x * (9/x2)
S = x2 + 36/x
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Daniel read several pages of a book on Saturday. He only reads 12 pages on sunday which was 25% less than what she read on Saturday. How many pages did Daniel read on Saturday.
Find an expression which represents the sum of (3x+9y) and (5x+7y) in simplest forms
The sum of the expression in simplest form is 8( x + 2y)
What are algebraic expressions?Algebraic expressions are expressions made up of variables, terms, factors, constants and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc
Given the expressions;
(3x+9y) and (5x+7y)
Let's find the sum
3x + 9y + 5x + 7y
collect like terms
3x + 5x + 9y + 7y
8x + 16y
Find common factor
8( x + 2y)
Thus, the sum of the expression in simplest form is 8( x + 2y)
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Calculate the coordinates of the points where the line y = 1 - 2x cuts the curve x^2+ y^2 = 2
Answer:
[tex](1, -1)[/tex] and [tex](-\frac{1}{5}, \frac{7}{5})[/tex]
In decimal form this would be (1, -1) and (-0.2, 1.4)
Step-by-step explanation:
Basically here we are trying to solve a system of 2 equations. The first one is a straight line and the second is a circle. This can be done graphically and graph is attached. There will be two points where the line cuts the circle so two solution sets
The equations are
Line Equation [tex]y = 1 - 2x[/tex] (1) and
Circle Equation [tex]x^2+ y^2 = 2[/tex] (2)
[tex]y=1-2x[/tex]
Plug this value of y into the second equation for the circle
[tex]x^2 + (1-2x)^2= 2[/tex]
Apply the perfect squares formula [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]
[tex](1-2x)^2 = 1^2-2\cdot \:1\cdot \:2x+\left(2x\right)^2\\= 1-4x+4x^2\\\\[/tex]
So equation (2) becomes
[tex]1-4x+4x^2 +x^2 = 2 \\\\\\5x^2 -4x - 1 = 0[/tex]
Solve using the quadratic formula
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here a is the coefficient of x ², b is the coefficient of x and c is the constant
So
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)}}{2\cdot \:5}[/tex]
Now,
[tex]\sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)} = \sqrt{\left(-4\right)^2+4\cdot \:5\cdot \:1}[/tex]
= [tex]\sqrt{16+20} = \sqrt{36} = 6[/tex]
Therefore
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \:6}{2\cdot \:5}[/tex]
[tex]x_1=\frac{-\left(-4\right)+6}{2\cdot \:5}[/tex] = [tex]\frac{-\left(-4\right)+6}{2\cdot \:5} =[/tex] [tex]\frac{10}{2\cdot \:5}[/tex] [tex]= 1[/tex]
[tex]x_2 = \frac{-\left(-4\right)-6}{2\cdot \:5}[/tex] [tex]= \frac{4-6}{2\cdot \:5}[/tex] = [tex]-\frac{1}{5}[/tex]
To find corresponding values for [tex]y_1 y_2[/tex] plug these values of [tex]x_1, x_2[/tex] into the line equation
[tex]y_1 = 1- 2(1) = -1[/tex]
[tex]y_2 = 1 - 2(-\frac{1}{5}) = 1 + \frac{2}{5} = \frac{7}{5}[/tex]
So the two points of intersection are
[tex](1, -1)[/tex] and ([tex](-\frac{1}{5}, \frac{7}{5})[/tex].
In decimal form this would be (1, -1) and (-0.2, 1.4)
See attached graph
Can you help solve this problem?
Answer:
22 and 23
Step-by-step explanation:
The first step is to make an equation that models this problem. Since the two numbers are consecutive, make them [tex]x[/tex] and [tex]x+1[/tex].
Since it says three times the larger number is 47 more than the smaller number, that means
[tex]3 (x+1) = x+47[/tex]
[tex]3x+3 = x+47[/tex]
[tex]2x+3=47[/tex]
[tex]2x=44[/tex]
[tex]x=22[/tex]
The smaller number is 22, and the larger number is 23.
Solve the inequality below for
Answer:
[tex]p ≤6[/tex]
Step-by-step explanation:
Inequality: [tex] - 4p +36 ≥2p[/tex]
Collect like terms
→ [tex] - 4p - 2p≥ - 36[/tex]
→ [tex] - 6p≥ - 36[/tex]
Divide both sides by -6
→ [tex] \frac{ - 6p}{ - 6}≤\frac{ - 36}{ - 6} [/tex]
Therefore: [tex]p ≤6[/tex]
I hope this helpsSimplify the polynomial expression. (1/2x +2)(1/2-2x)+(1/4x+7/2)
Simplifying the given polynomial expression is; -(1/4)x³ - (7/2)x² + (214/16)x + (7/2)
How to Simplify Polynomial Expressions?We want to simplify the polynomial expression;
((1/2)x + 2)((1/2) - 2x) + ((1/4)x + (7/2))
Let us expand the first bracket to get;
((1/2)x * (1/2) + (2 * (1/2)) - ((1/2)x * 2x) - (2 * 2x))
⇒ (1/4)x + 1 - x² - 4x
⇒ 1 + (15/4)x - x²
Thus, our expression is now;
(1 + (15/4)x - x²)((1/4)x + (7/2))
This can be multiplied out to give;
(1/4)x + (15/16)x - (1/4)x³ + (7/2) + (105/8)x - (7/2)x²
= -(1/4)x³ - (7/2)x² + (107/8)x + (15/16)x + (7/2)
= -(1/4)x³ - (7/2)x² + (214/16)x + (7/2)
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What’s the y and c intercept
Answer:
x - intercept; (80, 0)
y - intercept; (0, ∞)
Step-by-step explanation:
Let Week be w and Amount be A;
We see an inverse proportionality;
[tex]{ \rm{w \: \alpha \: \frac{1}{A } }} \\ \\ { \rm{w = \frac{m}{A} }}[/tex]
m is a constant of proportionality;
When w is 1, A = 68
[tex]{ \rm{ 1 = \frac{m}{68} }} \\ \\ { \rm{m = 68}}[/tex]
Therefore;
[tex]{ \tt{w = \frac{68}{A} + c }} \\ [/tex]
c is a constant;
When w is 0, A is 80
[tex]{ \rm{0 = \frac{68}{80} + c}} \\ \\ { \rm{c = - \frac{17}{20} }}[/tex]
Overall equation:
[tex]{ \rm{y = \frac{68}{x} + \frac{17}{20} }} \\ [/tex]
For x-intercept, y = 0
[tex]{ \rm{ \frac{17}{20} = \frac{68}{x} }} \\ \\ { \rm{x = 80}}[/tex]
For y-intercept, x = 0
y = ∞
A change in temperature of 6°C is equivalent to a change in temperature of
°F.
Define overlapping.
Answer:
to extend over or past and cover a part of The roof shingles overlap each other. 2 : to have something in common with Baseball season overlaps the football season in September. 1 : to occupy the same area in part The two towns overlap.
Step-by-step explanation:
here are the points on the graph that im finding slope to 3 , 135 and 5 ,225 and 7, 315
EDIT I FOUND THE ANSWER
The slope of the line having points (3,135), (5,225), and (7,315) is 45
Slope:
The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).
The formula of slope for a line(m)=[tex]\frac{y2-y1}{x2-x1}[/tex]
Given the points (3,135) , (5,225) and (7,315)
Consider any two points, Let's say (3,135) and (5,225).
Slope=[tex]\frac{225-135}{5-3}[/tex]
Slope=45
Therefore, The slope of the line having points (3,135), (5,225), and (7,315) is 45
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PLEASE HELP !! 51 POINTS !!
Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given.
Student A
Step 1: cosecant theta over cosecant theta minus sine theta over cosecant theta
Step 2: 1 minus sine theta over the quantity 1 over sine theta end quantity
Step 3: 1 − sin2 θ
Step 4: cos2 θ
Student B
Step 1: the quantity 1 over sine theta end quantity minus sine theta over the quantity cosecant theta
Step 2: the quantity 1 minus sine squared theta end quantity over sine theta all over cosecant theta
Step 3: cosine squared theta over sine squared theta
Step 4: cot2 θ
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)
Answer:
Student B
Step 1: the quantity 1 over sine theta end quantity minus sine theta over the quantity cosecant theta
Step 2: the quantity 1 minus sine squared theta end quantity over sine theta all over cosecant theta
Step 3: cosine squared theta over sine squared theta
Step 4: cot2 θ
Step-by-step explanation:
Jim and Henry have played 41 tennis matches.
Jim has won 23 times.
Henry won the rest.
a) Estimate the probability that Jim wins.
b) Estimate the probability that Henry wins.
Answer:
a) The probability that Jim wins is 0.56.
b) The probability that Henry wins is 0.44.
Step-by-step explanation:
Hope this helps!
When Arjun makes strawberry milk, he adds 90\,\text{mL}90mL90, start text, m, L, end text of milk for every 20\text{ mL}20 mL20, start text, space, m, L, end text of strawberry syrup. Arjun's brother, Eli, adds 180\,\text{mL}180mL180, start text, m, L, end text of milk for every 45\text{ mL}45 mL45, start text, space, m, L, end text of strawberry syrup.
Which strawberry milk has a stronger strawberry taste?
Eli's strawberry milk has a stronger strawberry taste than Arjun.
According to the question we have been given that
Arjun , adds milk = 90ml
in strawberry syrup = 20ml
Eli, adds milk = 180ml
in strawberry syrup = 45ml
We need to find whose strawberry milk has stronger strawberry taste that is we have to find the concentration of the solution.
The formula for the concentration is given as :
Concentration of the solution = [tex]\frac{volume of solute}{volume of solution}[/tex] * 100%
For Arjun,
Volume of solvent = 90ml
Volume of solute = 20ml
Volume of solution = 20+90 ml = 110 ml
Concentration = (20/110)*100%
= 18.18%
For Eli,
Volume of solvent = 180ml
Volume of solute = 45ml
Volume of solution = 180+45 ml = 225 ml
Concentration = (45/225)*100%
= 20%
As we can see that the Eli's concentration of the solution is greater than Arjun's. Hence Eli's strawberry milk has a stronger strawberry taste.
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Please show work, and brainliest will be yours.
the other statements are.
Converse: If it has a perimeter of 10 cm, then the figure is a rectangle with sides of 2 cm and 3 cm (false)Inverse: If the figure is not a rectangle with sides of 2 cm and 3 cm, then it has a perimeter different than 10cm (false)Contrapositive: "If it has a perimeter different than 10cm, then it is not a rectangle with sides of 2cm and 3cm" (true)How to get the converse, inverse, and contrapositive statements?
For a conditional statement of the form:
If P, then Q
The other statements are:
Converse: if Q then PInverse: not P, then not Q.Contrapositive: not Q, then not P.Here the conditional is:
"if a figure is a rectangle with sides 2 cm and 3cm, then it has a perimeter of 10cm"
We can identify:
P = a figure is a rectangle with sides 2 cm and 3cm
Q = it has a perimeter of 10cm
Then the other statements are.
Converse: If it has a perimeter of 10 cm, then the figure is a rectangle with sides of 2 cm and 3 cmThis clearly is false, as we can have a circle with a perimeter of 10 cm.
Inverse: If the figure is not a rectangle with sides of 2 cm and 3 cm, then it has a perimeter different than 10cmThis is also false, the figure can be a rectangle with sides of 1cm and 4 cm for example.
Contrapositive: "If it has a perimeter different than 10cm, then it is not a rectangle with sides of 2cm and 3cm"This is true. if the figure does not have a perimeter of 10cm, then it can't be a rectangle with sides of 2cm and 3cm
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.......................
Answer:
Step-by-step explanation:
6.92
Carlos read 150 words in one minute. He
read 5 times as many words as his younger
brother. How many words did his younger brother
read in one minute?
Answer:
30
Step-by-step explanation:
150/5 = 30
Answer: 30
Step-by-step explanation:
Carol Heinrich has lateral filing cabinets that need to be placed along the wall of a storage closet. The filing are each 1 1/2 feet wide and the wall is. 6 feet long. Decide how many cabinets can be placed along the wall
The number of cabinets that can be placed along the wall is 15.
How to calculate the value?It should be noted that in this scenario, we simply have to calculate the perimeter.
This will be:
= 2(length + width)
= 2(1 1/2 + 6)
= 2(7 1/2)
= 15
Therefore, the number of cabinets that can be placed along the wall is 15.
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ASAP
the actual distance on a map is 50km and on the map it corresponds to 4cm on map
Answer:
1 cm : 12.5 m
Step-by-step explanation:
Answer: 1250000:1
Step-by-step explanation:
Scale factor: 50 km/4 cm=25 km/2 cm
25 km/2 cm=
(25 * 1000 m)/(2 * 1/100 m)= ==> convert to common measurement which is meters.
(25000 m)/(2/100 m)=
(25000*100 m)/(2*100/100 m)=
2500000 m/2 m=1250000/1
how do you get the 40-4=36units, can you explain
Evan is thinking of a number that contains the digit 2. The digit 2 in Evan's number has 10 times the value of the digit 2 in the number 328,907.
Which number could be the number that Evan is thinking of?
Answer:
Evan could be thinking of 200,000.
Step-by-step explanation:
The digit 2 in 328,907 has values 20,000 so in Evan's number it has the values 200,000.
Which fraction is greater than -2/3 and less than -1/2?? Please help!! Thank you!!
first of all let's recall that on the negative side of the number line, the closer to 0, the greater, so -1 is much greater than -1,000,000.
well, let's simply try to convert both fractions to the same denominator by multiplying top and bottom by 1 or namely the same value, hmmm let's multiply -2/3 by 2/2 = 1, and -1/2 by 3/3 = 1
[tex]-\cfrac{2}{3}\cdot \cfrac{2}{2}\implies -\cfrac{4}{6}\hspace{5em}-\cfrac{1}{2}\cdot \cfrac{3}{3}\implies -\cfrac{3}{6}[/tex]
well, rats, no much wiggling room there, well, let's simply multiply them again by 1, in this case hmmmm 2/2 for both
[tex]-\cfrac{4}{6}\cdot \cfrac{2}{2}\implies \boxed{-\cfrac{8}{12}}\hspace{5em}-\cfrac{3}{6}\cdot \cfrac{2}{2}\implies \boxed{-\cfrac{6}{12}} \\\\\\ \underset{-\cfrac{2}{3}}{\boxed{-\cfrac{8}{12}}}\hspace{5em} < \qquad -\cfrac{7}{12}\qquad < \hspace{5em} \underset{-\cfrac{1}{2}}{\boxed{-\cfrac{6}{12}}}[/tex]
PLEASE HELP URGENT
If m<4=37°, find m<1,m<2,m<3
i would need a photo of the lines to find the values of other angles
The cost of 4 boxes of pens and 3 boxes of pencils is $22.55. The cost of 3 boxes of pens and 2 boxes of pencils is $16.45. Find the cost of each.
Answer:
One pen is $4.25 and one pencil is $1.85.
Step-by-step explanation:
Let cost of pens be x and cost of pencils be y.
1. 4x+3y=22.55
2. 3x+2y=16.45
Sub. 1.-2.,
x+y=22.55-16.45
x=6.1-y
Sub. x=6.1-y into 1.,
y=1.85
x=4.25
Answer:
Cost of a box of pens = $4.25
Cost of a box of pencils = $1.85
Step-by-step explanation:
Given information:
Cost of 4 boxes of pens and 3 boxes of pencils = $22.55Cost of 3 boxes of pens and 2 boxes of pencils = $16.45Define the variables:
Let x = the cost of a box of pens.Let y = the cost of a box of pencils.Create two equations from the given information:
[tex]\textsf{Equation 1}: \quad 4x + 3y = 22.55[/tex]
[tex]\textsf{Equation 2}: \quad 3x + 2y = 16.45[/tex]
Multiply Equation 1 by 3:
[tex]\implies 3 \cdot 4x + 3 \cdot 3y = 3 \cdot 22.55[/tex]
[tex]\implies 12x + 9y = 67.65[/tex]
Multiply Equation 2 by 4:
[tex]\implies 4 \cdot 3x + 4 \cdot 2y = 4 \cdot 16.45[/tex]
[tex]\implies 12x + 8y = 65.80[/tex]
Subtract the equations to eliminate the term in x:
[tex]\begin{array}{r rr}& 12x+9y = &67.65\\- & 12x+8y = &65.80\\\cline{2-3} & y = & 1.85\end{array}[/tex]
Substitute the found value of y into one of the equations and solve for x:
[tex]\implies 3x + 2y = 16.45[/tex]
[tex]\implies 3x + 2(1.85) = 16.45[/tex]
[tex]\implies 3x + 3.7 = 16.45[/tex]
[tex]\implies 3x =12.75[/tex]
[tex]\implies x=4.25[/tex]
Solution
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